We analyse data from seismic stations surrounding the Alboran Sea between Spain and North Africa to constrain variations of the lithosphere-asthenosphere boundary (LAB) in the region. The technique used is the receiver function technique, which uses S-to-P converted teleseismic waves at the LAB below the seismic stations. We confirm previous data suggesting a shallow (60-90 km) LAB beneath the Iberian Peninsula and we observe a similarly shallow LAB beneath the Alboran Sea where the lithosphere becomes progressively thinner towards the east. A deeper LAB (90-100 km) is observed beneath the Betics, the south of Portugal and Morocco. The structure of the LAB in the entire region does not seem to show any indication of subduction related features. We also observe good P receiver function signals from the seismic discontinuities at 410 and 660 km depth which do not indicate any upper-mantle anomaly beneath the entire region. This is in agreement with the sparse seismic activity in the mantle transition zone suggesting the presence of only weak and regionally confined anomalies.